Trying to focus on moving targets (like this little duckling photographed at the New York Botanical Garden) is tough. The minute you think you have them in focus, wham, they're gone before you can trip the shutter. Instead, try putting your camera in manual focus and focus on a spot where the action is repeating itself--home plate in a baseball game or the top of a piling where a seagull keeps landing and taking off, for example.
That's just what I did for this shot. I tried (and failed) about a dozen times as this duckling kept hopping up on the lily leaf and then--just as quickly--slipped back into the water. But once I put the lens in manual focus and focused on the center of the lily pad, all I had to do was wait for the duckling and fire when she came into the frame. I had the camera on a tripod and locked down tightly, so I didn't even have to watch through the viewfinder. I just kept my eye on the lily pad and then fired whenever she hopped up there. I also used a very fast shutter speed (1/1000 second) which was easy since the sun was very bright. Not only did the shutter speed stop the baby duck, but look how it froze the water on the leaf and the crop coming out off of the beak!
By the way, even if you are shooting with a camera that doesn't have a manual-focus mode, you can still use this technique. Just frame the spot where you want to focus and press the shutter release button halfway down (and hold it halfway down); that locks the focus (and exposure) and then when your subject comes into the frame, press the shutter release the rest of the way.
Interestingly, many of the forms of action we photograph do repeat themselves in some predictable way and predicting where and when that action will occur is the key to photographing it sharply. If you just pause for a few moments and study the scene before you start to shoot you'll have a good idea of where you need to focus and how often the subjects will come into the frame.
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